Effects of isotopic disorder on the Raman spectra of crystals: theory and ab initio calculations for diamond and germanium

Isotopic disorder is possibly the simplest phenomenon that breaks translati onal invariance in a crystal, thus lifting the selection rules due to the c onservation of crystal momentum. As a consequence of this symmetry lowering , the position, width, and shape of the Raman line in elemental semiconduct ors depends on isotopic composition. In this work the effects of isotopic d isorder on the Raman spectra of elemental semiconductors are studied 'exact ly' using a newly developed theoretical method which does not rely on any k ind of mean-held approximation. We first determine the interatomic force co nstants using density-functional perturbation theory; disorder effects are then simulated using very large super-cells of up to 60 000 atoms; the spec tral function which determines the Raman intensity is finally calculated vi a a reciprocal-space variant of the recursion method. We present theoretica l results obtained for diamond and germanium, and compare them with existin g theoretical data. (C) 2000 Elsevier Science B.V. All rights reserved.